An essential prerequisite for a commercial accumulation of hydrocarbons is the existence of a reservoir. For a rock to act as a reservoir, the rock must have two essential properties: it must have pores to contain the oil or gas (porosity); and the pores must be connected to allow the movement of fluids (permeability).
Porosity .phi. can be expressed as a volume ratio, which is the ratio of voids (pore space) to solid rock (matrix), or more frequently as a percentage: ##EQU1##
The pores can contain connate water, but within a field, contain oil or gas as well. Thus, porous reservoir rocks are a mixture of a solid (rock) and two fluid phases (hydrocarbon and water). The relative percentage of hydrocarbon or water in the pores of a reservoir rock is described as oil or water saturation respectively. In making decisions relative to the production of a field, it is important to know the hydrocarbon content (volume). Generally, the quantitative calculation of the hydrocarbon content of a reservoir is approached by first calculating the water saturation S.sub.w. Then oil saturation can be determined for example, as (1-S.sub.w).
Resistivity measurements can be used to calculate water saturation S.sub.w using Archie's Water Saturation Equation: EQU S.sub.w.sup.n =R.sub.o /R.sub.t =.sigma..sub.t /.sigma..sub.o, (1)
where n is the Archie Saturation Exponent, R.sub.o is the resistivity of formation rock 100% saturated with water (.sigma..sub.o being the corresponding conductivity), and R.sub.t is the resistivity of noninvaded partially saturated formation rock (.sigma..sub.t being the corresponding conductivity). Resistivity tools have been extensively used and, accordingly, Archie saturation exponents, total porosity, and other values which can be determined from resistivity logging are available or can be readily obtained or determined by those skilled in the art.
Archie saturation exponents can, for example, be determined from core measurements. Typically, cores are saturated with a simulated formation brine and the resistivity measured to determine R.sub.o. The saturated cores can then have part of the water removed by any of several known techniques and the resistivity R.sub.t at a partially water saturated condition can be measured. The value of water saturation of the core can be determined gravimetrically and Archie's equation can then be solved for n. This n value can be used to interpret resistivity measurements from downhole logging tools to determine the water saturation of petroleum reservoirs. All this is known to those skilled in the art and need not be further described here.
From Equation (1), it is apparent that the Archie Saturation Exponent n is representative of the influence of both hydrocarbon and water on water saturation since R.sub.t is the resistivity of partially saturated formation rocks, that is, the resistivity of rock containing both hydrocarbon and water.
Resistivity measurements cannot distinguish between formations containing fresh water and oil-bearing formations because fresh water and oil each have high resistivity (low conductivity). Dielectric logging tools were therefore developed for use in formations having fresh water to distinguish between water and hydrocarbons. Typically, dielectric logging tools measure formation dielectric permittivity using frequencies in the range from about 15 megahertz (MHz) to about 1.1 gigahertz (GHz), or more broadly from above 0 to about 1.3 GHz.
Dielectric logging tools can also be used to determine water saturation in formations of interest. Dielectric logs are able to distinguish between water and oil because the dielectric constant of water is between about 50-80 while for oil it is about 2. The rock matrix in which the oil and water are held has a dielectric constant between about 4-9. Thus, the large contrast in dielectric constant between water and oil and rock can be used to detect the presence of water in the rock pore spaces.
Increasingly, dielectric logging tools have been used in formations that contain, not fresh, but saline water (brine). Thus, for example, dielectric logging has been used to evaluate formations which have been subjected to waterflood because the waterflood can make it extremely difficult or impossible to obtain accurate data by use of resistivity logging tools. This is because the factor R.sub.t in the Archie Water Saturation Equation (1) above requires a determination of the resistivity of a noninvaded zone, that is, a region of the formation which has not been altered by invasion of nonformation fluids, and measurement of R.sub.t (resistivity of the noninvaded zone) by resistivity logging tools in formations which have been subjected to waterflooding is often just not feasible. Further, in many instances, water saturation S.sub.w is not directly determined from Equation (1) above, but by Equation (1a): ##EQU2## where .phi. is the porosity of the formation, m is the cementation exponent, R.sub.w is the resistivity of water present in the formation, and the remaining terms are as defined above. In formations which have been subjected to waterflooding, the value of R.sub.w as determined by resistivity measurements is frequently not reliable; hence dielectric logging, which is less sensitive to R.sub.w, is preferred.
Accordingly, in recent years it has become highly desirable to use dielectric logging measurements in formations which have widely varying saline contents, as well as in formations characterized by fresh water. However, the dielectric permittivity of a formation can vary with the frequency of the dielectric logging tool utilized, and also with the salinity of the formation fluids.
Thus, even though the dielectric permittivity of dry rock is essentially independent of frequency across the range of conventional dielectric logging tools, as is water, except for a slight effect above 1 GHz caused by dipole relaxation, when water and rock are combined, there is a frequency dependency in dielectric permittivity across the frequency range of dielectric logging tools.
Further, the dielectric permittivity .epsilon.* of a formation describes the electrical response of the formation materials to an applied electric field and contains a real part .epsilon.' (typically measured in farads/meter which describes the separation, or polarization, of electric charge), and an imaginary part .epsilon." which is descriptive of the flow of electric charge, for example, conductivity, resistivity, or the like. As a result, dielectric permittivities are influenced by the salinity of brine saturated rocks. This is because as salinity increases, the real part of the water permittivity decreases while water conductivity and the imaginary part of water dielectric permittivity increases. These changes in the water permittivity change the rock permittivity by increasing the apparent rock conductivity and in many cases, result in an increase in the real part of the rock permittivity. These changes due to salinity can also be frequency dependent.
A number of methods have been developed for determining oil and water saturation from dielectric permittivity data. For purposes of providing background to the invention hereinafter set forth, these methods can be categorized as methods which do not involve determining a measure of water filled porosity from the dielectric permittivity data and those which do involve such a determination. In regard to the latter, water is the dominant influence on the dielectric permittivity in water-filled or partially water-filled rock, even though the dielectric permittivity of the saturated rock is a combination of its constituent parts. Various models can be and are used to describe the constituent contributions to the total dielectric permittivity. Each model describes the volume percent of the constituent and a method for summing the constituents. Often these models can be solved for the individual volume percents of the constituents given the total and constituent values of the dielectric permittivity. Because the permittivity of rock and oil are similar, it can be assumed that only two constituents exist, rock and water, and the percent volumes of each sum to unity. EQU .phi..sub.rock +.phi..sub.water =1
The percent volume of water is referred to as the water-filled porosity .phi..sub.c. The actual value calculated for .phi..sub.c can vary from model to model and represents an apparent water-filled porosity based on the assumptions of the particular model used.
The following deal with methods of determining oil and water saturation from dielectric permittivity data which do not involve determining a measure of water filled porosity from dielectric permittivity data. Each of these methods moreover, is silent on the problem that water filled porosity determined from dielectric permittivity data often deviates significantly from directly measured water-filled porosity, and provides no technique or method for assessing the reliability of water-filled porosity or water saturation determined from dielectric permittivity data, or for causing water-filled porosity or water saturation thus determined to approximate actual or measured water-filled porosity or water saturation.
Fertl, U.S. Pat. No. 4,494,071 (1985) deals with determining water saturation in earth formations independent of lithology by obtaining base log measurements of the dielectric permittivity of the formations, then logging the formations a second time with the zone of investigation substantially 100% water saturated, and combining the base log measurements with the subsequent log measurements to provide a log of the water saturation of the formation which is substantially independent of lithology.
McKinlay, et al., U.S. Pat. No. 4,009,434 (1977) deals with a dielectric induction logging system for obtaining water and residual oil saturation of earth formations. The measured permittivity is then combined with porosity measurements, from another source, according to predetermined relationships and the water saturation determined. Thus, McKinlay, et al. do not determine porosity from dielectric permittivity data of porous reservoir rock, but require porosity known from other sources.
Hoyer, et al., U.S. Pat. No. 4,015,195 (1977) deals with a method of determining hydrocarbon saturation in a shaly formation by measuring dielectric constant at frequencies less than 50 kHz in first and second portions of the formation. Hoyer, et al. reports that the conductivity parameter of the formation is related to the dielectric constant and can be directly determined by correlating the measured dielectric constant with the relation between dielectric constant and the conductivity parameter. The Hoyer, et al. method deals with correcting for the effect of shale on conductivity, and the water saturation calculated from conductivity, by utilizing dielectric constant measurements made at a frequency of less than 50 kHz. The Hoyer, et al. method does not, however, calculate a water-filled porosity from the dielectric constant data.
The following deal with methods of determining oil and water saturation from dielectric permittivity data which do involve determining a measure of water-filled porosity from dielectric permittivity data.
Two methods for determining porosity from dielectric permittivity data, the Time Propagation Method (TPO) and the complex Refractive Index Method (CRI) (Wharton, et al., "Advancements in Electromagnetic Propagation Logging," SPE Paper 9041, 1980) are based upon the Lichtenecker-Rother (LR) Equation (Meador, et al., "Dielectric Constant Logging, A Salinity Independent Estimation of Formation Water Volume," SPE Paper 5504, 1975). (See also Wharton, et al., "Electromagnetic Propagation Logging: Advances in Technique and Interpretation, SPE Paper 9267.) These methods both assume a fixed geometrical distribution of formation and fluids consisting of layers in series and do not take into account the influence of a variable geometrical distribution of hydrocarbon and water in a porous reservoir rock, that is, the influence of a variable distribution of rock. Further, these methods are silent on the problem that porosity determined from dielectric permittivity data often deviates significantly from measued water-filled porosity, and provide no method or technique for assessing the reliability of porosity determined from dielectric permittivity data or for causing such porosity to approximate to true or measured water-filled porosity.
A third method is based upon the Hanai-Bruggeman Equation (HB) (Bussian, "Electrical Conducts in a Porous Medium," Geophysics, v. 48, no. 9, 1983, pp. 1258-1268; Sen, et al., "A Self-Similar Model for Sedimentary Rocks with Application to the Dielectric Constant of Fused Glass Beads," Geophysics, v. 46, no. 5, 1981, pp. 781-795) and differs in a fundamental way from the TPO and CRI Equations in that the HB Equation has an adjustable parameter known as the depolarization factor (L) to compensate for the variations in pore geometry that are present in rock formations. The depolarization factor (L) varies between 0 and 1 depending on the geometrical distribution of the constituent materials. The factor (L) can be determined for a particular reservoir by laboratory measurement using core samples, or can be estimated. In the laboratory, the constituent values for dielectric permittivity and waterfilled porosity can be determined and the HB Equation can be solved for the geometrical parameter L. By measuring L on a number of samples from a reservoir, a least squares regression on the L valus can be performed, and in many cases an L value representative of the reservoir can be obtained. Unlike the HB method, the TPO and CRI methods do not have an adjustable geometric factor such as (L). Accordingly, use of the HB Equation can increase the accuracy of porosity determination from dielectric permittivity data when core measurements are available to determine the depolarization factor. (See Sherman, "The Calculation of Porosity from Dielectric Constant Measurements: A Study Using Laboratory Data," SPWLA Paper, 1985, published in The Log Analyst, Vol. XXVII, No. 1, Jan.-Feb., 1986.) The factor (L), however, while it compensates for variations in pore geometry present in a rock formation, is determined experimentally from oil-filled or water-filled rocks, and hence does not take into account the influence of the variable geometric distribution of hydrocarbon and water in a porous earth formation. Compare also, Feng and Sen, "Geometrical Model of Conductive and Dielectric Properties of Partially Saturated Rocks," 58 J. APPL. PHYS. 3237-3243 (1985). By utilizing a twophase self-similar model, Feng and Sen simulate the dielectric constant .epsilon. of a rock by an equation (see Equation 11 in Feng and Sen) in which the porosity of the rock calculated from dielectric permittivity data is predicted to be the true water-filled porosity of the rock.
Thus, these methods which involve determining porosity from dielectric permittivity measurements, are silent on the problem that porosity determined from dielectric permittivity data often deviates significantly from directly measured water-filled porosity, and provide no technique or method for accessing the reliability of porosity determined from dielectric permittivity data or for causing porosity thus determined to approximate measured water-filled porosity.